The expected value of a function of a fuzzy variable with a continuous membership function (Q931756)

The expected value considered in this paper has nothing to do with some kind of expectation of a random variable. A less misleading expression would be: mean value or defuzzification of a fuzzy quantity. For defuzzification there are many proposals in the literature (most of them with a ranking-of-fuzzy-number background). In this paper, the authors consider a defuzzification proposal introduced by Liu which uses a credibility-measure background [see \textit{L. Liu}, ``Expected value of a fuzzy variable and fuzzy expected value model'', IEEE Trans. Fuzzy Syst. 10, 445--450 (2002)]. They consider monotonic functions of a fuzzy quantity with continuous membership function and present exact formulas for defuzzification.